Solve -2(-8x)/4=7(x^3)

Question

Solve the equation

x_{1} = - \frac{2 7}{7}, x_{2} = 0, x_{3} = \frac{2 7}{7}

Alternative Form

x_{1} \approx - 0.755929, x_{2} = 0, x_{3} \approx 0.755929

Evaluate

- (2 \times \frac{- 8 x}{4}) = 7 x^{3}

Simplify

More Steps

Evaluate

- (2 \times \frac{- 8 x}{4})

Divide the terms

More Steps

Evaluate

\frac{- 8}{4}

Reduce the numbers

\frac{- 2}{1}

Calculate

- 2

- (2 (- 2 x))

Multiply the numbers

More Steps

Evaluate

2 (- 2)

Multiplying or dividing an odd number of negative terms equals a negative

- 2 \times 2

Multiply the numbers

- 4

- (- 4 x)

Calculate

4 x

4 x = 7 x^{3}

Add or subtract both sides

4 x - 7 x^{3} = 0

Factor the expression

x (4 - 7 x^{2}) = 0

Separate the equation into 2 possible cases

x = 0 4 - 7 x^{2} = 0

Solve the equation

More Steps

Evaluate

4 - 7 x^{2} = 0

Move the constant to the right-hand side and change its sign

- 7 x^{2} = 0 - 4

Removing 0 doesn't change the value,so remove it from the expression

- 7 x^{2} = - 4

Change the signs on both sides of the equation

7 x^{2} = 4

Divide both sides

\frac{7 x ^{2}}{7} = \frac{4}{7}

Divide the numbers

x^{2} = \frac{4}{7}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm \frac{4}{7}

Simplify the expression

More Steps

Evaluate

\frac{4}{7}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{4}{7}

Simplify the radical expression

\frac{2}{7}

Multiply by the Conjugate

\frac{2 7}{7 \times 7}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2 7}{7}

x = \pm \frac{2 7}{7}

Separate the equation into 2 possible cases

x = \frac{2 7}{7} x = - \frac{2 7}{7}

x = 0 x = \frac{2 7}{7} x = - \frac{2 7}{7}

Solution

x_{1} = - \frac{2 7}{7}, x_{2} = 0, x_{3} = \frac{2 7}{7}

Alternative Form

x_{1} \approx - 0.755929, x_{2} = 0, x_{3} \approx 0.755929

Show Solution